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The explanatory indispensability argument [a] is an altered form of the Quine–Putnam indispensability argument in the philosophy of mathematics.It claims that we should believe in mathematical objects such as numbers because they are indispensable to scientific explanations of empirical phenomena.
According to Melia, we only need to believe in mathematics if it is indispensable to science in the right kind of way. In particular, it needs to be indispensable to scientific explanations. [69] But according to Melia, mathematics plays a purely representational role in science, it merely "[makes] more things sayable about concrete objects". [70]
The Indispensability of Mathematics [1] is a 2001 book by Mark Colyvan in which he examines the Quine–Putnam indispensability argument in the philosophy of mathematics.This thesis is based on the premise that mathematical entities are placed on the same ontological foundation as other theoretical entities indispensable to our best scientific theories.
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